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Trigonometric Function

Specified trigonometric function on input

  • Library:
  • Simulink / Math Operations

    HDL Coder / Math Operations

  • Trigonometric Function block

Description

The Trigonometric Function block performs common trigonometric functions and outputs the result in rad or rev.

Supported Functions

You can select one of these functions from the Function parameter list.

FunctionDescriptionMathematical Expression MATLAB® Equivalent
sin

Sine of the input

sin(u)

sin
cos

Cosine of the input

cos(u)

cos
tan

Tangent of the input

tan(u)

tan
asin

Inverse sine of the input

asin(u)

asin
acos

Inverse cosine of the input

acos(u)

acos
atan

Inverse tangent of the input

atan(u)

atan
atan2

Four-quadrant inverse tangent of the input

atan2(u)

atan2
sinh

Hyperbolic sine of the input

sinh(u)

sinh
cosh

Hyperbolic cosine of the input

cosh(u)

cosh
tanh

Hyperbolic tangent of the input

tanh(u)

tanh
asinh

Inverse hyperbolic sine of the input

asinh(u)

asinh
acosh

Inverse hyperbolic cosine of the input

acosh(u)

acosh
atanh

Inverse hyperbolic tangent of the input

atanh(u)

atanh
sincos

Sine of the input; cosine of the input

cos + jsin

Complex exponential of the input

CORDIC Approximation Method

If you use the CORDIC approximation method (see More About), the block input has further requirements.

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to CORDIC, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [–2π, 2π) rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0, 2π) rad.

When you set Function to atan2 and the Approximation method to CORDIC, the block has these limitations:

  • Inputs must be the same size, or at least one value must be a scalar value.

  • Both inputs must have the same data type.

  • When you use signed fixed-point types, the word length must be 126 or less.

  • When you use unsigned fixed-point types, the word length must be 125 or less.

This table summarizes what happens for an invalid input.

Block UsageEffect of Invalid Input
Simulation modesAn error appears.
Generated codeUndefined behavior occurs. Avoid relying on undefined behavior for generated code.

Lookup Approximation Method

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to Lookup, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [-2ᴨ,2ᴨ] rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0,2ᴨ) rad.

  • When you set Function to atan2 and the Approximation method to Lookup, the block has these limitations:

    • Inputs must be the same size, or at least one value must be a scalar value.

    • Both inputs must have the same data type.

    • The number of data points are limited by:

      • smallEnoughNumDataPoints = 2(inputFractionLen-2)+1

      • bigEnoughFractionLen = log2(numberOfDataPoints - 1)+2

      where:

      • smallEnoughNumDataPoints is the maximum number of data points represented by specified input fraction length, inputFractionLen.

      • bigEnoughFractionLen is the minimum fraction length needed to represent specified number of data points, numberOfDataPoints.

Ports

Input

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Input specified as a scalar, vector, or matrix. The block accepts input signals of the following data types:

FunctionsInput Data Types
  • sin

  • cos

  • sincos

  • cos + jsin

  • atan2

  • Floating point

  • Fixed point (only when Approximation method is CORDIC)

  • tan

  • asin

  • acos

  • atan

  • sinh

  • cosh

  • tanh

  • asinh

  • acosh

  • atanh

  • Floating point

Dependencies

  • When you set Function to atan2, the block shows two input ports. The first input (Port_1) is the y-axis or imaginary part of the function argument. The second input (Port_2) is the x-axis or real part of the function argument.

  • You can use floating-point input signals when you set Approximation method to None, CORDIC, or Lookup. However, the block output data type depends on which of these approximation method options you choose.

    Input Data TypeApproximation MethodOutput Data Type

    Floating point

    None

    Depends on your selection for Output signal type. Options are auto (same data type as input), real, or complex.

    Floating point

    CORDIC

    Same as input. Output signal type is not available when you use the CORDIC approximation method to compute the block output.

    Floating point

    Lookup

    Same as input. Output signal type is not available when you use the Lookup approximation method to compute the block output.

For CORDIC and Lookup approximations:

  • Input must be real for the sin, cos, sincos, cos + jsin, and atan2 functions.

  • Output is real for the sin, cos, sincos, and atan2 functions.

  • Output is complex for the cos + jsin function.

Limitations

Complex input signals are supported for all functions in this block except atan2.

You can use fixed-point input signals only when Approximation method is set to CORDIC or Lookup. The CORDIC and Lookup approximations are available for the sin, cos, sincos, cos + jsin, and atan2 functions.

CORDIC approximation fixed-point type propagations:

Input Data TypeFunctionOutput Data Type

Fixed point, signed or unsigned

sin, cos, sincos, and cos + jsin

fixdt(1, WL, WL - 2) where WL is the input word length

This fixed-point type provides the best precision for the CORDIC algorithm.

Fixed point, signed

atan2

fixdt(1, WL, WL – 3)

Fixed point, unsigned

atan2

fixdt(1, WL, WL – 2)

Lookup approximation fixed-point type propagations:

Input Data TypeFunctionOutput Data Type

Fixed point, signed

sin, cos, sincos, cos + jsin, atan2

fixdt(1, WL, FL)

Fixed point, unsigned

sin, cos, sincos, cos + jsin, atan2

fixdt(1, WL - 1, FL)

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to CORDIC, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [–2π, 2π) rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0, 2π) rad.

When you set Function to atan2 and the Approximation method to CORDIC, the block has these limitations:

  • Inputs must be the same size, or at least one value must be a scalar value.

  • Both inputs must have the same data type.

  • When you use signed fixed-point types, the word length must be 126 or less.

  • When you use unsigned fixed-point types, the word length must be 125 or less.

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to Lookup, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [-2ᴨ,2ᴨ] rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0,2ᴨ) rad.

  • When you set Function to atan2 and the Approximation method to Lookup, the block has these limitations:

    • Inputs must be the same size, or at least one value must be a scalar value.

    • Both inputs must have the same data type.

    • The number of data points are limited by:

      • smallEnoughNumDataPoints = 2(inputFractionLen-2)+1

      • bigEnoughFractionLen = log2(numberOfDataPoints - 1)+2

      where:

      • smallEnoughNumDataPoints is the maximum number of data points represented by specified input fraction length, inputFractionLen.

      • bigEnoughFractionLen is the minimum fraction length needed to represent specified number of data points, numberOfDataPoints.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Input the x-axis or real part of the function argument for atan2. When you set Function to atan2, the block shows two input ports. The first input (Port_1) is the y-axis or imaginary part of the function argument. The second input (Port_2) is the x-axis or real part of the function argument. (See Port Location After Rotating or Flipping for a description of the port order for various block orientations.)

Dependencies

To enable this port, set Function to atan2.

Limitations

  • Fixed-point input signals are supported only when you set Approximation method to CORDIC or Lookup.

  • When you set Function to atan2 and Approximation method to CORDIC:

    • Inputs must be the same size, or at least one value must be a scalar value.

    • Both inputs must have the same data type.

    • When you use signed fixed-point types, the word length must be 126 or less.

    • When you use unsigned fixed-point types, the word length must be 125 or less.

  • When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to Lookup, the block has these limitations:

    • When you use signed fixed-point types, the input angle must fall within the range [-2ᴨ,2ᴨ] rad.

    • When you use unsigned fixed-point types, the input angle must fall within the range [0,2ᴨ) rad.

  • When you set Function to atan2 and the Approximation method to Lookup, the block has these limitations:

    • Inputs must be the same size, or at least one value must be a scalar value.

    • Both inputs must have the same data type.

    • The number of data points are limited by:

      • smallEnoughNumDataPoints = 2(inputFractionLen - 2)+1

      • bigEnoughFractinoLen = log2(numberOfDataPoints - 1)+2

      where:

      • smallEnoughNumDataPoints is the maximum number of data points represented by specified input fraction length, inputFractionLen.

      • bigEnoughFractinoLen is the minimum fraction length needed to represent specified number of data points, numberOfDataPoints.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Output

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Result of applying the specified trigonometric function to one or more inputs in rad. Each function supports:

  • Scalar operations

  • Element-wise vector and matrix operations

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Sine of the input signal, in rad and rev.

Dependencies

To enable this port, set Function to sincos.

Limitations

Fixed-point input signals are supported only when you set Approximation method to CORDIC or Lookup.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Cosine of the input signal, in rad and rev.

Dependencies

To enable this port, set Function to sincos.

Limitations

Fixed-point input signals are supported only when you set Approximation method to CORDIC or Lookup.

Data Types: half | single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | fixed point

Parameters

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Specify the trigonometric function. The name of the function on the block icon changes to match your selection.

Limitations

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to CORDIC, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [–2π, 2π) rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0, 2π) rad.

When you set Function to atan2 and the Approximation method to CORDIC, the block has these limitations:

  • Inputs must be the same size, or at least one value must be a scalar value.

  • Both inputs must have the same data type.

  • When you use signed fixed-point types, the word length must be 126 or less.

  • When you use unsigned fixed-point types, the word length must be 125 or less.

Programmatic Use

Block Parameter: Operator
Type: character vector
Values: 'sin' | 'cos' | 'tan' | 'asin' | 'acos' | 'atan' | 'atan2' | 'sinh' | 'cosh' | 'tanh' | 'asinh' | 'acosh' | 'atanh' | 'sincos' | 'cos + jsin'
Default: 'sin'

Specify the type of approximation for computing output.

Approximation MethodData Types SupportedWhen to Use This Method
None (default)

Floating point

You want to use the default Taylor series algorithm.

CORDIC

Floating point and fixed point

You want a fast, approximate iterative calculation.

Lookup

Floating point and fixed point (double and single)

You want a fast, approximate lookup table implementation.

Dependencies

To enable this parameter, set Function to sin, cos, sincos, cos + jsin, or atan2.

To use fixed-point input signals, you must set Approximation method to CORDIC or Lookup.

Limitations

When you set Function to sin, cos, sincos, or cos + jsin and set the Approximation method to CORDIC, the block has these limitations:

  • When you use signed fixed-point types, the input angle must fall within the range [–2π, 2π) rad.

  • When you use unsigned fixed-point types, the input angle must fall within the range [0, 2π) rad.

When you set Function to atan2 and the Approximation method to CORDIC, the block has these limitations:

  • Inputs must be the same size, or at least one value must be a scalar value.

  • Both inputs must have the same data type.

  • When you use signed fixed-point types, the word length must be 126 or less.

  • When you use unsigned fixed-point types, the word length must be 125 or less.

Programmatic Use

Block Parameter: ApproximationMethod
Type: character vector
Values: 'None' | 'CORDIC' | 'Lookup'
Default: 'None'

Specify the number of iterations to perform the CORDIC algorithm. The default value is 11.

  • When the block input uses a floating-point data type, the number of iterations can be a positive integer.

  • When the block input is a fixed-point data type, the number of iterations cannot exceed the word length.

    For example, if the block input is fixdt(1,16,15), the word length is 16. In this case, the number of iterations cannot exceed 16.

Dependencies

To enable this parameter, you must set the Function and Approximation method parameters as follows:

  • Set Function to sin, cos, sincos, cos + jsin, or atan2.

  • Set Approximation method to CORDIC.

Programmatic Use

Block Parameter: NumberOfIterations
Type: character vector
Values: positive integer, less than or equal to word length of fixed-point input
Default: '11'

Specify the angle unit for lookup method as radian or revolution.

Dependencies

To enable this parameter:

  • Set Function to sin, cos, sincos, cos + jsin, or atan2.

  • Set Approximation method to Lookup.

Programmatic Use

Block Parameter: AngleUnit
Type: character vector
Values: 'radian' | 'revolution'
Default: 'radian'

Specify the number of data points for lookup table as a scalar real number.

Dependencies

To enable this parameter:

  • Set Function to sin, cos, sincos, cos + jsin, or atan2.

  • Set Approximation method to Lookup.

Programmatic Use

Block Parameter: NumberOfDataPoints
Type: character vector
Values: scalar
Default: '16'

Specify the output signal type of the Trigonometric Function block as auto, real, or complex.

FunctionInput Signal TypeOutput Signal Type
AutoRealComplex
Any selection for the Function parameter realrealrealcomplex
complexcomplexerrorcomplex

Dependencies

Setting Approximation method to CORDIC disables this parameter.

Note

When Function is atan2, complex input signals are not supported for simulation or code generation.

Programmatic Use

Block Parameter: OutputSignalType
Type: character vector
Values: 'auto' | 'real' | 'complex'
Default: 'auto'

For acos and asin, select this check box to remove the protection against out-of-range inputs, which reduces redundancy.

  • When you clear this check box, the protection is enabled. The block saturates out-of-range inputs to 1 or -1 before any operation is performed. Generated code contains code to check for out-of-range input.

  • When you select this check box, the protection is removed. The block performs all operations on the input value without any changes. Generated code does not contain code to check for the out-of-range input.

Enabling this check box can eliminate redundancy if the input is already in range.

Dependencies

Setting Function to acos and asin enables this parameter.

Programmatic Use

Block Parameter: RemoveProtectionAgainstOutOfRangeInput
Type: character vector
Values: 'off' | 'on'
Default: 'off'

Specify the sample time as a value other than -1. For more information, see Specify Sample Time.

Dependencies

This parameter is not visible unless it is explicitly set to a value other than -1. To learn more, see Blocks for Which Sample Time Is Not Recommended.

Programmatic Use

Block Parameter: SampleTime
Type: character vector
Values: scalar or vector
Default: '-1'

Block Characteristics

Data Types

double | fixed point[a] | half | integer[a] | single

Direct Feedthrough

yes

Multidimensional Signals

yes

Variable-Size Signals

yes

Zero-Crossing Detection

no

[a] This block supports fixed-point and base integer data types for 'Approximation method' CORDIC.

More About

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References

[1] Volder, Jack E., “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers EC-8 (1959); 330–334.

[2] Andraka, Ray “A Survey of CORDIC Algorithm for FPGA Based Computers.” Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays. Feb. 22–24 (1998): 191–200.

[3] Walther, J.S., “A Unified Algorithm for Elementary Functions,” Proceedings of the Spring Joint Computer Conference, May 18-20, 1971: 379–386.

[4] Schelin, Charles W., “Calculator Function Approximation,” The American Mathematical Monthly 90, no. 5 (1983): 317–325.

Extended Capabilities

PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.

See Also

Blocks

Functions

Introduced before R2006a